Corzine’s “Sgt. Schultz” defense at recent congressional hearings on the demise of MF Global and the looting of $1.6 billion from customer accounts seemed a brilliant way to avoid the embarrassment of taking the Fifth while also dodging any perjury trap.

By playing dumb on key questions, Corzine seemed to shield himself from the serious charge of lying under oath. But he did get specific about a few things — one of which is clearly contradicted by the recent trustee’s report on MF Global’s demise.

The former US senator and NJ governor — still a top Obama fund-raiser — could still be facing serious criminal charges. At the very least, it looks like he was trying to mislead Congress as it tried to get to the bottom of the MF Global mess.

In his answers, Corzine claimed ignorance of basic facts, particularly in key areas of firm compliance and controls — the divisions that were supposed to catch improper transfers of cash out of customer accounts. He said it was the job of underlings to know such facts and figures. Any mistakes, his testimony suggested, were those underlings’ fault.

He’d been assured, he said, that funds paid to creditors during the firm’s frantic final days “were properly transferred.” So went Corzine’s mantra at several Senate and House hearings. Until now, it seemed to have worked.

Corzine’s perjury problem begins when he was pushed on the issue of compliance and controls and what he did about them when he dramatically changed the firm’s business model.

Pre-Corzine, MF Global had been a pretty simple operation: It sold commodities to customers, many of them ranchers and farmers looking to hedge against livestock and crop price swings. Corzine aimed to ramp up profits by ramping up risk — jumping into high-octane trading in the global markets by taking bets like mega-banks Goldman Sachs and JP Morgan.

Goldman and Morgan have both suffered big trading losses over the years, but their strict compliance procedures always protected customer cash. Corzine was asked if MF Global, in its bid to be more like Goldman, had done the same.

Corzine testified that he’d have “trouble giving you the exact statistics” about the control personnel who were on the ground making sure customer money was safe. But then he did get specific, explaining that, yes, MF Global did enhance its compliance and control system to meet the challenges of its riskier business model: “We made changes, upgraded. We also installed a new technology system.”

Rep. Peter King (R-LI) pressed him, asking whether those changes included “new personnel or just reprograms of old personnel?”

Again Corzine was uncharacteristically specific, answering, “No. There were new people at it.”

That’s not what it says in the trustee’s report. The trustee, James Giddens, simply describes what Corzine and his top people did as “negligence.” Contrary to Corzine’s assurances under oath, Giddens said the much-needed upgrades to protect customer money under the new, riskier, business model never took place.

Or as Giddens put it: “Notwithstanding the increased demands on global money management and liquidity, the firm’s Treasury Department, which was involved in implementing the transfers of funds, did not expand or modernize . . . technology for recording and tracking transactions and liquidity did not materially change. These critical functions remained essentially as they had been prior to Mr. Corzine’s arrival.”

The problems that led to that loss of $1.6 billion in customer money had persisted off and on throughout Corzine’s tenure, because the “systems and tools that would enable accurate real-time monitoring of liquidity were never implemented.”

OK, perjury is tough to prove. In this case, says Peter Henning, a Wayne State University law professor and an expert in white-collar crime, prosecutors would need to show that Corzine’s testimony “was completely false.” If MF Global bought a new computer for compliance, that might be enough.

But, as former Securities and Exchange Commission Chairman Harvey Pitt says, “Whether the particular statement is perjurous depends not only on the truth or falsity of the statement but also on whether it misled Congress to its detriment. I think Corzine does run a risk that his statements — although carefully scripted — might ultimately be deemed perjurous in light of the trustee’s report.”

Bottom line: A serious prosecutor might well be able to make a case. Good thing for Corzine that all the federal prosecutors now work for his pal, President Obama.